Quantum mechanics question on probability amplitude

[spaghetti3451]

Homework Statement

What physical phenomenon requires us to work with probability amplitudes rather than just
with probabilities, as in other fields of endeavour?

Homework Equations

The Attempt at a Solution

That the probability of an outcome is given by the square of the modulus of the corresponding probability amplitude? But that's not a physical phenomenon?

 

[dikmikkel]

Is probability a physical phenomenon? I don't think so, but maybe.
Like any statistical distribution you can use the density to e.g. finding the probability of the particle being a point in space:
Find the probability that the electron has position x = 2 given that:
$p(x) = |\psi(x)|^2 = 1/x^2$
Then you would be wrong to integrate, but simply doing this would solve it:
$p(x=2) = 1/2^2 = 4$
I don't think you can assign much meaning to the $\psi(x)$ alone.
Hope that helped a little.

 

[dextercioby]

'Waves superposition' would be an answer.